Is (tan(x))/(sec(x)+1)=csc(x)-cot(x) ?

The answer to whether (tan(x))/(sec(x)+1)=csc(x)-cot(x) is True

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prove (tan(x))/(sec(x)+1)=csc(x)-cot(x)

prove

\frac{tan ( x )}{sec ( x ) + 1} = csc (x) - cot (x)

True

Solution steps

\frac{tan ( x )}{sec ( x ) + 1} = csc (x) - cot (x)

Manipulating left side

\frac{tan ( x )}{sec ( x ) + 1}

Express with sin, cos

= \frac{sin ( x )}{1 + cos ( x )}

Manipulating right side

csc (x) - cot (x)

Express with sin, cos

= \frac{1 - cos ( x )}{sin ( x )}

Rewrite using trig identities

= \frac{sin ( x )}{1 + cos ( x )}

We showed that the two sides could take the same form

\Rightarrow True

cos^{2} (x) = \frac{1}{sec ^{2} ( x )}

\frac{( 1 + tan ( θ ) )}{1 + cot ( θ )} = tan (θ)

1 + \frac{cos ^{2} ( x )}{1 + sin ( x )} = sin (x)

sec^{2} (x) (1 - csc^{2} (x)) = - csc^{2} (x)

- sin^{2} (x) = cos^{2} (x) - 1

Is (tan(x))/(sec(x)+1)=csc(x)-cot(x) ?
The answer to whether (tan(x))/(sec(x)+1)=csc(x)-cot(x) is True